AN APPROACH FOR CONSTRUCTING NONISOSPECTRAL HIERARCHIES OF EVOLUTION-EQUATIONS

For a given isospectral (lambda(t) = 0) hierarchy of evolution equations, we propose a simple method of constructing its corresponding non-isospectral (lambda(t) = lambda(n), n greater-than-or-equal-to 0) hierarchy of evolution equations closely related to tau-symmetries. It is crucial to find an initial Lax operator W0 and an initial vector field go satisfying the key equation [W0, L] = L'[g0] - I, in which L, i are spectral and identity operators, respectively. As examples, we present the corresponding non-isospectral hierarchies of equations and display the fundamental relations generating symmetry algebras for KdV hierarchy, AKNS hierarchy and a new integrable hierarchy.